OLCCONVEXITY
Updated: 30 June 2014
Use OLCCONVEXITY to calculate the convexity for a bond that has an odd last coupon. Convexity is defined as the second derivative of price with respect to yield divided by the dirty price of the bond multiplied by 100.
Syntax
SELECT [wctFinancial].[wct].[OLCCONVEXITY](
<@Settlement, datetime,>
,<@Maturity, datetime,>
,<@LastCouponDate, datetime,>
,<@Rate, float,>
,<@Yld, float,>
,<@Redemption, float,>
,<@Frequency, float,>
,<@Basis, nvarchar(4000),>)
Arguments
@Settlement
the settlement date of the security. @Settlement is an expression that returns a datetime or smalldatetime value, or a character string in date format.
@Maturity
the maturity date of the security. @Maturity is an expression that returns a datetime or smalldatetime value, or a character string in date format.
@LastCouponDate
the last coupon date of the security. The period from the last coupon date until the maturity date defines the odd interest period. The quasimaturity date is assumed to occur at a regular periodic interval as defined by @Frequency and @Basis. @LastCouponDate is an expression that returns a datetime or smalldatetime value, or a character string in date format.
@Rate
the bond’s annual coupon rate. @Rate is an expression of type float or of a type that can be implicitly converted to float.
@Yld
the yield for the maturity date passed into the function. @Yld is an expression of type float or of a type that can be implicitly converted to float.
@Redemption
the redemption value of the bond assuming a par value of 100. @Redemption is an expression of type float or of a type that can be implicitly converted to float.
@Frequency
the number of coupon payments per year. For annual payments, @Frequency = 1; for semiannual, @Frequency = 2; for quarterly, @Frequency = 4; for bimonthly @Frequency = 6; for monthly @Frequency = 12. For bonds with @Basis = 'A/364' or 9, you can enter 364 for payments made every 52 weeks, 182 for payments made every 26 weeks, 91 for payments made every 13 weeks, 28 for payments made every 4 weeks, 14 for payments made every 2 weeks, and 7 for weekly payments. @Frequency is an expression of type float or of a type that can be implicitly converted to float.
@Basis
is the type of day count to use. @Basis is an expression of the character string data type category.
@Basis

Day count basis

0, 'BOND'

US (NASD) 30/360

1, 'ACTUAL'

Actual/Actual

2, 'A360'

Actual/360

3, 'A365'

Actual/365

4, '30E/360 (ISDA)', '30E/360', 'ISDA', '30E/360 ISDA', 'EBOND'

European 30/360

5, '30/360', '30/360 ISDA', 'GERMAN'

30/360 ISDA

6, 'NL/ACT'

No Leap Year/ACT

7, 'NL/365'

No Leap Year /365

8, 'NL/360'

No Leap Year /360

9, 'A/364'

Actual/364

10, 'BOND NONEOM'

US (NASD) 30/360 nonendofmonth

11, 'ACTUAL NONEOM'

Actual/Actual nonendofmonth

12, 'A360 NONEOM'

Actual/360 nonendofmonth

13, 'A365 NONEOM'

Actual/365 nonendofmonth

14, '30E/360 NONEOM', '30E/360 ICMA NONEOM', 'EBOND NONEOM'

European 30/360 nonendofmonth

15, '30/360 NONEOM', '30/360 ISDA NONEOM', 'GERMAN NONEOM'

30/360 ISDA nonendofmonth

16, 'NL/ACT NONEOM'

No Leap Year/ACT nonendofmonth

17, 'NL/365 NONEOM'

No Leap Year/365 nonendofmonth

18, 'NL/360 NONEOM'

No Leap Year/360 nonendofmonth

19, 'A/364 NONEOM'

Actual/364 nonendofmonth

Return Type
float
Remarks
· If @Maturity <= @Settlement 0 is returned.
· If @Settlement is NULL, @Settlement = GETDATE()
· If @Rate is NULL, @Rate = 0
· If @Yld is NULL, @Yld = 0
· If @Frequency is NULL, @Frequency = 2
· If @Basis is NULL, @Basis = 0.
· If @Frequency is any number other than 1, 2, 4, 6 or 12, or for @Basis = 'A/364' any number other than 1, 2, 4, 6, or 12 as well as 7, 14, 28, 91, 182, or 364 OLCCONVEXITY returns an error.
· If @Basis is invalid (see above list), OLCCONVEXITY returns an error.
· @Rate is entered as a decimal value; 1.0% = 0.01
· @Yld is entered as a decimal value; 1.0% = 0.01
· If @Maturity is NULL an error will be returned.
· If @IssueDate is NULL an error will be returned.
· If @LastCouponDate is NULL an error will be returned.
Examples
This is a bond with an odd short last coupon period where the settlement date in the last coupon period.
SELECT
wct.OLCCONVEXITY(
'20141001', @Settlement
'20141215', @Maturity
'20140915', @Last_interest
0.0225, @Rate
0.0010, @Yield
100, @Redemption
2, @Frequency
1 @Basis
) as Convexity
This produces the following result.
Convexity

0.000858134852128336
This is a bond with an odd long last coupon period with a settlement date in the last coupon period.
SELECT
wct.OLCCONVEXITY(
'20141001', @Settlement
'20141215', @Maturity
'20140315', @Last_interest
0.0225, @Rate
0.0010, @Yield
100, @Redemption
2, @Frequency
1 @Basis
) as Convexity
This produces the following result.
Convexity

0.000858134847371233
This is a bond with an odd short last coupon with a settlement date prior to the last coupon date.
SELECT
wct.OLCCONVEXITY(
'20141001', @Settlement
'20341215', @Maturity
'20340915', @Last_interest
0.0425, @Rate
0.0400, @Yield
100, @Redemption
2, @Frequency
1 @Basis
) as Convexity
This produces the following result.
Convexity

2.3881623279505
This is a bond with an odd long last coupon period with a settlement date prior to the last coupon date.
SELECT
wct.OLCCONVEXITY(
'20141001', @Settlement
'20341215', @Maturity
'20340315', @Last_interest
0.0425, @Rate
0.0400, @Yield
100, @Redemption
2, @Frequency
1 @Basis
) as Convexity
This produces the following result.
Convexity

2.38892585231749
This is an example of a bond paying interest every 26 weeks.
SELECT
wct.OLCCONVEXITY(
'20141004', @Settlement
'20141215', @Maturity
'20140601', @Last_interest
0.1250, @Rate
0.1100, @Yield
100, @Redemption
182, @Frequency
9 @Basis
) as CONVEXITY
This produces the following result.
CONVEXITY

0.000749542121966884
See Also